In algebraic geometry, the Stein factorization, introduced by Karl Stein (1956) for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking, Stein factorization contracts the connected components of the fibers of a mapping to points.
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geometry, the Steinfactorization, introduced by Karl Stein (1956) for the case of complex spaces, states that a proper morphism can be factorized as a composition...
triangular matrices). Let A be a square matrix. An LU factorization refers to the factorization of A, with proper row and/or column orderings or permutations...
from a compact space to a Hausdorff space is a closed subset. The Steinfactorization theorem states that any proper morphism to a locally noetherian scheme...
matching with the factorization labels in turn. Similarly add three more blocks 12CDEF, 34CDEF, and 56CDEF, replacing the factorization labels by the corresponding...
although there are many different ways of finding a factorization using an integer factorization algorithm, they all must produce the same result. Primes...
as it is an analog of a fiber space in algebraic topology. By the Steinfactorization, any surjective projective morphism is a contraction morphism followed...
variety. A deep property of proper morphisms is the existence of a Steinfactorization, namely the existence of an intermediate scheme such that a morphism...
essential step in several integer factorization algorithms, such as Pollard's rho algorithm, Shor's algorithm, Dixon's factorization method and the Lenstra elliptic...
arithmetic, that every (positive) integer has a factorization into a product of prime numbers, and this factorization is unique up to the ordering of the factors...
limit. The theorem is used to deduce some other important theorems: Steinfactorization and a version of Zariski's main theorem that says that a proper birational...
integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought...
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor...
factorize the DFT similarly to Cooley–Tukey but without the twiddle factors. The Rader–Brenner algorithm (1976) is a Cooley–Tukey-like factorization but...
straightforward computation allows verifying that the existence of this factorization is equivalent with Δ 0 = Δ 1 = 0. {\displaystyle \Delta _{0}=\Delta...
then given as a factorization of the matrix Q = Γ T Γ {\displaystyle Q=\Gamma ^{\mathsf {T}}\Gamma } (e.g. the Cholesky factorization) and is considered...
function, as defined below (Rudin 1987, Thm 17.17). This "Beurling factorization" allows the Hardy space to be completely characterized by the spaces...
few hundred points". Shortly afterwards, Ulam, with collaborators Myron Stein and Mark Wells, used MANIAC II at Los Alamos Scientific Laboratory to extend...
number of variables is fixed (in 1983); Discovering the elliptic curve factorization method (in 1987); Computing all solutions to the inverse Fermat equation...
from a given and principal parts (Cousin I problem), and Weierstrass factorization theorem was able to create a global meromorphic function from a given...
rings, the ideal class number, which measures the failure of unique factorization, is given in OEIS A003649; for the imaginary case, they are given in...
not assured in arbitrary integral domains. However, if R is a unique factorization domain, then any two elements have a GCD, and more generally this is...
scale names are standard in the English-speaking world.) Its prime factorization is 2 100 × 5 100 . {\displaystyle 2^{100}\times 5^{100}.} The term was...
Is public-key cryptography possible? Log-rank conjecture Can integer factorization be done in polynomial time on a classical (non-quantum) computer? Can...
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